What is the Least Common Multiple of 85728 and 85743?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 85728 and 85743 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85728 and 85743, than apply into the LCM equation.

GCF(85728,85743) = 3
LCM(85728,85743) = ( 85728 × 85743) / 3
LCM(85728,85743) = 7350575904 / 3
LCM(85728,85743) = 2450191968

Least Common Multiple (LCM) of 85728 and 85743 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85728 and 85743. First we will calculate the prime factors of 85728 and 85743.

Prime Factorization of 85728

Prime Factorization of 85743

Now multiplying the highest exponent prime factors to calculate the LCM of 85728 and 85743.

LCM(85728,85743) = 2⁵ × 3² × 19¹ × 47¹ × 7¹ × 1361¹
LCM(85728,85743) = 2450191968